The normal on led bulbs is they are polarity specific... indeed they are diodes.

if its turning on, is indeed on correct polarity, JUST maybe is not using the correct led bulb replacement.

asuming is an old Mopar which uses the 1004 bulb, needs to be sure you are getting the correct bulb replacement with filaments/emissors isolated from socket and just getting both poles throught the contacts on base. NOT ANY 2 CONTACTS BULB WILL WORK!!! 1057 bulbs for example seems to work being dual contacts BUT NOT! they get ground by the socket and the socket on dome light is attached to the body, so ANY of the contacts getting positive will make it light up and won't turn off ever being, as described previouslly, the dome light is switched on/off via negative/Ground and positive being constant from batt!